A238232 -id:A238232 - cp's OEIS frontend

A239205 Numbers k such that sigma(k) divides the sum of the numbers x coprime to k, with x <= k.

28, 140, 190, 248, 420, 477, 496, 672, 840, 910, 1428, 1488, 1547, 1638, 1848, 1892, 2295, 2398, 2480, 2660, 3417, 3472, 3515, 3640, 3720, 4064, 4095, 4590, 4641, 4655, 4845, 5456, 5655, 5995, 6200, 6678, 6888, 6944, 7030, 7440, 8008, 8128, 8190, 9214, 9282

Offset: 1

Paolo P. Lava, Mar 12 2014

Numbers k such that sigma(k) | k*phi(k)/2.

			28 is a term since 28*phi(28)/2 = 168, sigma(28) = 56 and 168 / 56 = 3.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from Paolo P. Lava)

Cf. A000010, A000203, A238232, A239208.

with(numtheory); P:=proc(q) local a,n;
for n from 1 to q do a:=n*phi(n)/2; if type(a/sigma(n),integer) then print(n);
fi; od; end: P(10^6);

Select[Range[10^4], Divisible[# * EulerPhi[#]/2, DivisorSigma[1, #]] &] (* Amiram Eldar, Mar 03 2020 *)

A239208 Numbers n such that sigma(n) divides the sum of the numbers x not coprime to n, with x<=n.

Original entry on oeis.org

18, 135, 891, 4095, 10560, 13120, 14144, 21600, 23199, 74655, 144495, 192311, 404415, 4197375, 4612608, 5675775, 6664680, 9180800, 10953215, 11110400, 14381055, 18162144, 18420480, 18920000, 20765024, 25159680, 32058351, 41055200, 55889920, 65327104, 65982464

Offset: 1

Paolo P. Lava, Mar 12 2014

Numbers n such that sigma(n) | n/2(n+1-phi(n)).

			18/2*(19-phi(18)) = 117, sigma(18) = 39 and 117 / 39 = 3.

Giovanni Resta, Table of n, a(n) for n = 1..100

Cf. A000010, A000230, A238232, A239205.

with(numtheory); P:=proc(q) local a,n;
for n from 1 to q do a:=n/2*(n+1-phi(n)); if type(a/sigma(n),integer) then print(n);
fi; od; end: P(10^6);

a(14)-a(31) from Giovanni Resta, Mar 12 2014

cp's OEIS Frontend

A239205 Numbers k such that sigma(k) divides the sum of the numbers x coprime to k, with x <= k.

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